arXiv subjects

Madhurendra Mishra

Publications and source records attributed to Madhurendra Mishra.

7 recordsLinked to original sources

arXiv2026

Chemical Frequency Combs in Reaction-Diffusion Oscillators

Frequency combs, evenly spaced spectral lines locked to one fundamental frequency, are well known in optics and have also been found in phononic, magnonic, ferroelectric, and cosmological systems, but have not yet been studied in oscillating chemical reactions. In this work, we show that reaction-diffusion oscillators can also produce frequency combs. We use the Brusselator model and derive its Hopf bifurcation condition directly from the rate equations. We find that the trimolecular autocatalytic term is the only source of nonlinear harmonic content. Above the Hopf threshold, our simulations of target-wave patterns show a clear fundamental frequency followed by a long, evenly spaced ladder of harmonics, with each harmonic weaker than the one before it. We then vary the reactant concentrations and kinetic parameters one at a time and find that this comb structure holds across a wide range of values. We also test this idea experimentally using the Belousov-Zhabotinsky reaction. Intensity signals recorded at different points in a target pattern show a shared fundamental frequency with several weakening harmonics, matching the simulated pattern closely. Together, these results show that reaction-diffusion chemistry is a new platform for generating frequency combs.

nlin.PS↗

arXiv2026

On the Nonlinear Sensitivity of Phononic Frequency Combs to Physical Perturbations

Phononic frequency combs offer a rich platform for nonlinear sensing, yet how their observable properties respond to changes in physical parameters remains poorly understood. Using a reduced two-mode autoparametric resonance model, we investigate how primary and secondary detuning, drive amplitude, and relative damping jointly shape amplitude and frequency sensitivity across the nonlinear parameter space. We find that sensitivity is far from uniform: primary detuning shifts the comb response smoothly, secondary detuning produces sharply localized transitions near resonance manifolds, and drive amplitude concentrates peak sensitivity close to the activation threshold rather than deep within the comb state. The relative damping redistributes energy continuously between modes without introducing discontinuities. The nonlinear sensitivity of amplitude and frequency observables across all parameters points to a common physical origin in autoparametric resonance, nonlinear saturation, and coupling-induced synchronization, offering a coherent basis for designing nonlinear sensing platforms with deliberate, parameter-aware sensitivity engineering.

nlin.PS↗

arXiv2026

Financial Frequency Combs

Frequency combs are discrete, equally spaced, phase-coherent spectral lines that emerge from nonlinear mode coupling in physical systems. We show that the incommensurate fractional-order financial model of Huang, Li, Ma, and Chen, whose Caputo derivatives encode macroeconomic long-range memory, generates an analogous structure in its steady-state spectrum. The comb appears only over specific values and ranges of the saving amount $a$, the investment cost $b$, and the demand elasticity $c$, outside which the spectral lines lose their equal spacing. It persists across extended parameter regimes and stays invariant to perturbations in the initial interest rate $x_0$ and investment demand $y_0$, while distinct spectral regimes appear at different initial price levels $z_0$. The comb is generated only when the fractional-order exponents $q_1$, $q_2$, and $q_3$ associated with interest rate, investment demand, and price index are above the critical threshold values. At even higher values of these exponents, the frequency comb transitions into chaos. These findings show that the long-run cyclic structure of a memory-bearing financial economy organises into a discrete, deterministic spectral fingerprint rather than a stochastic continuum.

nlin.PS↗

arXiv2026

Nonlinear Dynamical Regimes of Cosmological Frequency Combs

We study the emergence of Cosmological Frequency Combs (CFCs) in a quintessence cosmology with an exponential potential using a dynamical systems formulation. Expressing the evolution equations in expansion-normalized variables yields an autonomous nonlinear system that supports time-periodic attractors corresponding to limit cycles, producing comb like spectral structures in cosmological observables without external periodic forcing. Numerical simulations reveal transitions between single frequency, comb like and chaotic regimes controlled by the fundamental frequency, background equation of state parameter, and initial conditions. Coherent comb structures arise only within well defined dynamical windows, while very low frequencies and unfavorable initial conditions suppress phase locking. These results show that CFCs naturally emerge from nonlinear cosmological dynamics and motivate further study of their possible observational implications.

astro-ph.CO↗

arXiv2026

Information Is Not Physical: Possibility Spaces, Erasure, and the Structure of Unrealized Alternatives

The slogan ``information is physical,'' introduced by Rolf Landauer and developed through quantum information theory and black-hole thermodynamics, has achieved near-axiomatic status in modern physics. Yet the ontological status of information remains surprisingly underexamined: most discussions either reduce information to a form of energy or treat it as a purely mathematical object. This paper proposes a third position. I argue that information is neither a physical substance nor a free-floating abstraction, but rather \emph{the structure of physically realizable alternatives} -- a counterfactual structure that a physical system instantiates in virtue of the possibility space available to it. Building on Shannon's combinatorial definition, the Landauer principle, the no-cloning theorem, and the black-hole information paradox, I show that the informational content of any physical event is constituted by the set of outcomes that \emph{could have occurred} but did not. This counterfactual reading dissolves several persistent confusions: it explains why erasing information dissipates heat without making information ``material,'' why quantum superposition is informationally richer than any classical mixture, and why information loss in black holes is physically significant beyond mere bookkeeping. The proposal sits within a structural-realist framework but departs from standard structural realism by locating the relevant structure in modal, not merely actual, relations. I conclude by sketching implications for the foundations of quantum mechanics, quantum gravity, and scientific ontology more broadly.

physics.hist-ph↗

arXiv2026

Multi-Tongue Frequency Fractal Dynamics in Hodgkin-Huxley Neurons Induced by Temporal Interference Stimulation

We investigate neuronal excitability in the Hodgkin-Huxley model under temporal interference (TI) stimulation in a previously unexplored sub-Hz resonant regime and uncover a striking nonlinear response that we term 'multi-tongue frequency fractals'. Unlike single-frequency driving, which yields a smooth resonant valley, dual-frequency excitation fragments this response into a hierarchy of sharply modulated tongues whose number and structure grow with observation time, revealing clear self-similar architecture. These features emerge from transitions between non-cascaded and cascaded high-harmonic and sub-harmonic generation as detuning varies, and are maximized near the intrinsic ionic timescale at omega ~ 0.2 rad/s. Parameter sweeps show that the fractal count is higher for higher potassium conductances, lower sodium conductances and lower leak conductances. These results demonstrate that TI stimulation can elicit rich, hierarchically organized frequency responses even in classical excitable membranes, revealing fractal organization in Hodgkin-Huxley dynamics.

nlin.PS↗

arXiv2025

Cosmological Frequency Combs

We identify a new class of time periodic attractor solutions in scalar field cosmology, which we term Cosmological Frequency Combs (CFC). These solutions arise in exponential quintessence models with a phantom matter background and exhibit coherent phase-locked oscillations in the scalar field's normalized variables. We demonstrate that such dynamics induce modulations in observables like the Hubble parameter and growth rate, offering a dynamical mechanism to even address the H0 tension exactly. Our results uncover a previously unexplored phase of cosmic acceleration, linking the concept of frequency combs to large scale cosmological evolution.

astro-ph.CO↗